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In the wake of the GOP upset in the U.S. Senate race in Massachusetts, a new public poll finds California’s Democratic Sen. Barbara Boxer – thanks to a big advantage among women – clinging to a narrow 4-point lead over Republican Tom Campbell, who entered the race only two weeks ago.

The survey, from the Public Policy Institute of California, also shows Democratic Attorney General Jerry Brown – trailing among men but leading among women — with a slim 5-point advantage over Meg Whitman, the Republican former CEO of eBay.

The results mirror those reported last week by the Field Poll, but with closer margins than the earlier survey: Field had Boxer and Brown each with 10-point leads over Campbell and Whitman.

Both widely respected, the two polls use wholly different sampling methods to determine who is a likely voter. Another key factor: the distribution of voters by age in the Field Poll is considerably older – and closer to our projections — than in the PPIC survey.*

In the GOP Senate primary field, Campbell leads with 27% of the likely voters, followed by former Hewlett-Packard CEO Carly Fiorina at 16% and Assemblyman Chuck DeVore at 8%. Interestingly, Campbell holds an 8-point edge over Fiorina among men but a 14-point lead over her among women. Nearly half of GOP voters — 48% — remain undecided in the Senate race, PPIC reported.

Boxer has long run better among women than among men, and the findings in the PPIC survey underscore that dynamic.

Against Campbell, Boxer is trailing among men, 40-46%, but leads among women, 50-36%. Against DeVore, Boxer loses the men 41-45% but carries women 53-33%. And against Fiorina, Boxer loses men 41-46% but interestingly has her largest margin among women – 55-33%.

Against all three challengers, she takes about eight in 10 Democrats while they capture eight in 10 Republicans. But Boxer holds an important lead among the independents: 42-37% over Campbell, 45-35% over Fiorina and 45-34% over DeVore. Assuming either Boxer or her challenger holds his or her partisans, the battle in the Senate race will come down to who can carry the independents.

This is where Campbell – who is pro-choice, pro-gay rights and moderate on the environment – could, with significant resources, pose a more serious threat to Boxer than either Fiorina or DeVore.

Over in the GOP primary for governor, Whitman, who held a 20-point lead over Campbell in December, before he switched races, now holds a 30-point lead over Insurance Commissioner Steve Poizner, her lone remaining major rival.

Even with 41% of the vote compared to Poizner’s 11%, however, an additional 44% of the GOP primary voters remain undecided.

The PPIC findings also suggest Whitman has a problem among women voters, much like the Field Poll showed. For example, Whitman leads Poizner by 35 points (48-13%) among men in the primary vote but by 25 points – one-third less – among women (34-9%).

In the primary, that’s a gender difference but in a general election match-up against Jerry Brown, it’s a genuine gender gap: It’s Whitman over Brown 43-38% among men but Brown over Whitman 44-30% among women. That’s a 19-point gender gap in Brown’s favor against the woman GOP candidate, giving Brown his overall 41-36% edge over Whitman.

The same is not true for a Brown-Poizner match-up: he leads Poizner 43-34% among men and 46-24% among women for an overall advantage of 44-29%.

Other findings in the PPIC poll:

Most Californians would be willing to pay higher taxes to maintain current funding for public schools and most favor spending cuts in prisons and corrections . . .

But while majorities want to protect K–12 schools and cut spending on prisons, Californians are as divided as their leaders on the overall strategy to deal with the state’s $20 billion budget deficit: 41 percent favor a mix of spending cuts and tax increases and 37 percent favor mostly spending cuts (9% favor mostly tax increases).

They are in more agreement when it comes to asking the federal government for help, as Governor Arnold Schwarzenegger has done: 66 percent say California should seek federal aid to help meet its budget obligations.

PPIC surveyed 2,001 California adults Jan. 12-19, including 1,223 respondents deemed to be likely voters or whom 445 were identified as likely voters in the Republican primary. The margin of error for the overall survey is ±2 percent at the 95 percent confidence level, ±3 percent for likely voters and ±5 percent for the GOP primary.

* The differences between Field and PPIC are significant. Field calls only registered voters from the voter file and uses past voting behavior in the file to determine who is a likely voter; PPIC calls households at random (thereby reaching households with unlisted numbers) and asks people if they are registered and likely to vote.

Field’s callers know how people are registered — Democrat, Republican, Decline to State or Other; PPIC asks people to tell them. Field makes voters who only use a cell phone (younger voters) a key part of their survey; PPIC includes 200 cell phone users but not necessarily people who have no land line.

One result: While 45% of likely voters in the Field Poll are age 55 and older, just 39% of the voters in the PPIC poll are in that age bracket. Because Brown has a powerful advantage among older voters, his percentages are likely understated in the PPIC survey. (BTW, the Calbuzz estimate, based on our experience and extensive review with pollsters and analysts, is that 59% of the electorate in November will be age 50 and older and about 46% will be age 55 and older.)